feat(frontends/lean): improve coercion manangement

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/frontends/lean/frontend.cpp

@@ -379,47 +379,75 @@ struct lean_extension : public environment_extension {
         return !n.is_atomic() && get_explicit_version(n.get_prefix()) == n;
     }
 
+    /**
+        \brief It is too expensive to normalize \c t when checking if there is a coercion for it.
+        So, we just do a 'quick' normalization following a chain of definitions.
+    */
+    expr coercion_type_normalization(expr t, ro_environment const & env) const {
+        while (true) {
+            if (is_constant(t)) {
+                auto obj = env->find_object(const_name(t));
+                if (obj && obj->is_definition()) {
+                    t = obj->get_value();
+                } else {
+                    return t;
+                }
+            } else {
+                return t;
+            }
+        }
+    }
+
     void add_coercion(expr const & f, environment const & env) {
         expr type      = env->infer_type(f);
         expr norm_type = env->normalize(type);
         if (!is_arrow(norm_type))
             throw exception("invalid coercion declaration, a coercion must have an arrow type (i.e., a non-dependent functional type)");
-        expr from      = abst_domain(norm_type);
+        expr from      = coercion_type_normalization(abst_domain(norm_type), env);
-        expr to        = abst_body(norm_type);
+        expr to        = coercion_type_normalization(abst_body(norm_type), env);
         if (from == to)
             throw exception("invalid coercion declaration, 'from' and 'to' types are the same");
-        if (get_coercion(from, to))
+        if (get_coercion_core(from, to))
             throw exception("invalid coercion declaration, frontend already has a coercion for the given types");
         m_coercion_map[expr_pair(from, to)] = f;
         m_coercion_set.insert(f);
-        list<expr_pair> l = get_coercions(from);
+        list<expr_pair> l = get_coercions_core(from);
         insert(m_type_coercions, from, cons(expr_pair(to, f), l));
         env->add_neutral_object(new coercion_declaration(f));
     }
 
-    optional<expr> get_coercion(expr const & from_type, expr const & to_type) const {
+    optional<expr> get_coercion_core(expr const & from_type, expr const & to_type) const {
         expr_pair p(from_type, to_type);
         auto it = m_coercion_map.find(p);
         if (it != m_coercion_map.end())
             return some_expr(it->second);
         lean_extension const * parent = get_parent();
         if (parent)
-            return parent->get_coercion(from_type, to_type);
+            return parent->get_coercion_core(from_type, to_type);
         else
             return none_expr();
     }
 
-    list<expr_pair> get_coercions(expr const & from_type) const {
+    optional<expr> get_coercion(expr const & from_type, expr const & to_type, ro_environment const & env) const {
+        return get_coercion_core(coercion_type_normalization(from_type, env),
+                                 coercion_type_normalization(to_type, env));
+    }
+
+    list<expr_pair> get_coercions_core(expr const & from_type) const {
         auto r = m_type_coercions.find(from_type);
         if (r != m_type_coercions.end())
             return r->second;
         lean_extension const * parent = get_parent();
         if (parent)
-            return parent->get_coercions(from_type);
+            return parent->get_coercions_core(from_type);
         else
             return list<expr_pair>();
     }
 
+    list<expr_pair> get_coercions(expr const & from_type, ro_environment const & env) const {
+        return get_coercions_core(coercion_type_normalization(from_type, env));
+    }
+
     bool is_coercion(expr const & f) const {
         if (m_coercion_set.find(f) != m_coercion_set.end())
             return true;
@@ -555,10 +583,10 @@ void add_coercion(environment const & env, expr const & f) {
     to_ext(env).add_coercion(f, env);
 }
 optional<expr> get_coercion(ro_environment const & env, expr const & from_type, expr const & to_type) {
-    return to_ext(env).get_coercion(from_type, to_type);
+    return to_ext(env).get_coercion(from_type, to_type, env);
 }
 list<expr_pair> get_coercions(ro_environment const & env, expr const & from_type) {
-    return to_ext(env).get_coercions(from_type);
+    return to_ext(env).get_coercions(from_type, env);
 }
 bool is_coercion(ro_environment const & env, expr const & f) {
     return to_ext(env).is_coercion(f);

tests/lean/bad8.lean

@@ -0,0 +1,9 @@
+Variable list : Type → Type
+Variable nil {A : Type} : list A
+Variable cons {A : Type} (head : A) (tail : list A) : list A
+Variable a : ℤ
+Variable b : ℤ
+Variable n : ℕ
+Variable m : ℕ
+Definition l1 : list ℤ := cons a (cons b (cons n nil))
+Definition l2 : list ℤ := cons a (cons n (cons b nil))

tests/lean/bad8.lean.expected.out

@@ -0,0 +1,11 @@
+  Set: pp::colors
+  Set: pp::unicode
+  Assumed: list
+  Assumed: nil
+  Assumed: cons
+  Assumed: a
+  Assumed: b
+  Assumed: n
+  Assumed: m
+  Defined: l1
+  Defined: l2